cp's OEIS Frontend

A284415 Number of self-avoiding planar walks of length n starting at (0,0), ending on the x-axis, remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1) with the restriction that (0,1) is never used below the diagonal and (1,0) is never used above the diagonal.

%I A284415 #19 Oct 09 2019 13:34:49
%S A284415 1,1,3,5,14,34,96,259,748,2142,6329,18727,56358,170370,520354,1596980,
%T A284415 4935307,15319460,47794472,149681904,470620062,1484513696,4697619876,
%U A284415 14906459690,47426014833,151247657528,483426998881,1548323383749,4968516324954,15972198595374
%N A284415 Number of self-avoiding planar walks of length n starting at (0,0), ending on the x-axis, remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1) with the restriction that (0,1) is never used below the diagonal and (1,0) is never used above the diagonal.
%H A284415 Alois P. Heinz, <a href="/A284415/b284415.txt">Table of n, a(n) for n = 0..516</a>
%H A284415 Alois P. Heinz, <a href="/A284415/a284415.gif">Animation of a(6)=96 walks</a>
%H A284415 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_path">Lattice path</a>
%H A284415 Wikipedia, <a href="https://en.wikipedia.org/wiki/Self-avoiding_walk">Self-avoiding walk</a>
%F A284415 a(n) = Sum_{j=floor((sqrt(1+8*n)-1)/2)..n} A284414(j,n).
%Y A284415 Column sums of A284414.
%Y A284415 Cf. A001006, A003056.
%K A284415 nonn,walk
%O A284415 0,3
%A A284415 _Alois P. Heinz_, Mar 26 2017